30 research outputs found
Qualitative results for a relativistic wave equation with multiplicative noise and damping terms
No full textWave equations describing a wide variety of wave phenomena are commonly seen in mathematical physics. The inclusion of a noise term in a deterministic wave equation allows neglected degrees of freedom or fluctuations of external fields describing the environment to be considered in the equation. Moreover, adding a noise term to the deterministic equation reveals remarkable new features in the qualitative behavior of the solution. For example, noise can lead to singularities in some equations and prevent singularities in others. Taking into account the effects of the fluctuations along with a space-time white noise, we consider a relativistic wave equation with weak and strong damping terms and investigate the effect of multiplicative noise on the behavior of solutions. The existence of local and global solutions is provided, and some qualitative properties of solutions, such as continuous dependence of solutions on initial data, and blow up of solutions, are given. Moreover, an upper bound is provided for the blow up time.</p
Global existence and nonexistence of solutions for a Klein-Gordon equation with exponential type nonlinear term
No full textIn this paper, the global existence and nonexistence of solutions for a Klein-Gordon equation, appearing in a variety of physical situations, with exponential typesource term and supercritical initial energy (E(0) > d) are investigated in a boundeddomain. In the framework of the potential well, a functional including both of initial datais defined, and by sign invariance of this functional, the global existence of weak solutionsin the case of the high initial energy is proved. Moreover, under some conditions imposedon initial displacement and initial velocity, a finite time blow-up result is provided whichextends a result given in the literature.</p
HeatMapper Expansion
No full textExpansion of an existing visualization tool for genomic data.Software TechnologyElectrical Engineering, Mathematics and Computer Scienc
Predict Radiotherapy Plan Quality
No full textA person with cancer has several treatment options. One of which is radiotherapy. Radiotherapy is treatment of cancer with radiation. To minimize the damage to healthy tissue, radiation is applied from several directions into the body. When treating cancer with radiotherapy, the organs nearby the tumor are at high risk of getting damaged. In the treatment plan the dose to the organs at risk has to be balanced with the dose given to the target. These calculations are nowadays done by medical personnel. Although a lot of treatments succeed, without much damage to healthy tissue, a lot of treatments do serious damage to the organs at risk. Can treatment plans be optimized in terms of organ sparing? To reach optimization, several methods have been executed in order to create groups within a patient set. 115 patients of prostate cancer have been analyzed using Principal Component Analysis and Agglomerative Clustering. The data consist of Overlap Volume Histogram values of the bladder and rectum in a CSV file. Each CSV file contains 201 values. These CSVs are used as an input for both methods. This led to several figures as results. The principal component analysis showed that 80% of the data is covered by the first principal component and 92% by the first and second. Also, a scatterplot has been made, which shows the transformed data. This scatterplot shows no subgroups can be identified with the bladder and rectum data of the patient. The Agglomerative Clustering method results in six plots. A variation in linkages and connectivity has been used, but all six led to no clear distinction within the data. These results led to the conclusion that no subgroups are distinguishable based only on OVH data and no prediction can be made that optimizes radiotherapy plans based solely on OVH data of patients.Intelligent SystemsElectrical Engineering, Mathematics and Computer Scienc
Existence of global solutions for a multidimensional Boussinesq-type equation with supercritical initial energy
No full text1st International Conference on Analysis and Applied Mathematics (ICAAM) -- OCT 18-21, 2012 -- Gumushane, TURKEYIn this work, global weak solutions of the multidimensional Boussinesq-type equation with power type nonlinearity gamma vertical bar u vertical bar(p), gamma > 0 and supercritical initial energy is given by potential well method. Classical energy methods can not guarantee the global existence for this type of nonlinearity. As is known the functional I (u) defined for potential well method includes only the initial displacement, and by use of sign invariance of this functional one can only prove the global existence for critical and subcritical initial energy. In the case of supercritical initial energy such a functional fails to prove the global existence. A new functional is defined, which contains not only initial displacement, but also initial velocity.Sci & Technol Res Council Turkey (TUBITAK),Gumushane Univ,Fatih Uni
On the Existence of Global Solutions for a Nonlinear Klein-Gordon Equation
No full textThe aim of this work is to study the global existence of solutions for the Cauchy problem of a Klein-Gordon equation with high energy initial data. The proof relies on constructing a new functional, which includes both the initial displacement and the initial velocity: with sign preserving property of the new functional we show the existence of global weak solutions
Existence results for a nonlinear Timoshenko equation with high initial energy
No full textInternational Conference on Advancements in Mathematical Sciences (AMS) -- NOV 05-07, 2015 -- Antalya, TURKEYThe aim of the present paper is to study the initial -boundary value problem for a nonlinear Timoshenko equation with high energy initial data. Existence of global weak solutions is proved by sign preserving property of a new functional which is introduced for the potential well method.Fatih Univ,Badji Mokhtar Annaba Univ,Inst Math & Math Modelin
Global existence and decay of solutions for the generalized bad Boussinesq equation
No full textIn this paper, we consider the global existence of solutions for the Cauchy problem of the generalized sixth order bad Boussinesq equation. Moreover, we show that the supremum norm of the solution decays algebraically to zero as (1 + t)(-(1/7)) when t approaches to infinity, provided the initial data are sufficiently small and regular
